On growth of meromorphic solutions of nonlinear difference equations and two conjectures of C.C. Yang

In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equationsf^(z)n+_{P n-1}(f)= 0,where n ≤ 2 and P_n-1(f) is a difference polynomial of degree at most n - 1 in f with small functions as coefficients. Moreover, we give two examples to show that one conjecture proposed by Yang and Laine [2] does not hold in general if the hyper-order of f(z) is no less than 1.